Figure 4

Experimental PDFs for P and \(P^2\): probability distribution functions for P (a) and \(P^2\) (b) raised from the experimental data of the shoal’s polarization time series for the same number of fish used in Fig. 2 for fully uncorrelated shoals. For small N there is a clear tendency towards larger polarizations. For large N the PDFs evolve towards Rayleigh (PDF for P) and exponential (PDF for \(P^2\)) but with widths larger than in the corresponding PDFs for uncorrelated shoals with the same number of fish.